SOLUTION: A plane traveled 644 miles each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 14 hours. What is th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A plane traveled 644 miles each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 14 hours. What is th      Log On


   

Question 1155140: A plane traveled 644 miles each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 14 hours. What is the speed of the plane in still air? What is the speed of the wind?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
r, speed of plane with no wind
w, wind speed
G, the time going
2G, the time back
D, one-way distance
-
G=7
D=644

system%28r%2Bw=D%2FG%2Cr-w=D%2F%282G%29%29
.
.
highlight%28r=%283D%29%2F%284G%29%29

r=%283%2A644%29%2F%284%2A7%29
highlight%28highlight%28r=69%29%29-------speed for plane when no wind

highlight%28highlight%28w=23%29%29-------speed of wind

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The speed with the wind was 644/7 = 92mph; the speed against the wind was 644/14 = 46mph.

Solve the rest of the problem using logical reasoning and simple arithmetic.

The speed of the wind added to the speed of the plane is 92mph; the speed of the wind subtracted from the speed of the plane is 46mph.

That means the speed of the plane is halfway between 46mph and 92mph: 69mph.

And that means the speed of the wind was 69-46 = 23mph.